Physics - Sound Wave Question with Solution | TestHub

$\mathrm{V}=$speed of sound and$\mathrm{L}=$lenght of pipes

For open pipe first overtone${\mathrm{f}}_1=\frac{\mathrm{V}}{\mathrm{L}}$

For closed pipe first overtone$\mathrm{f}{\text{'}}_1=\frac{3\mathrm{V}}{4\mathrm{L}}$

$\therefore {\mathrm{f}}_1-\mathrm{f}{\text{'}}_1=\frac{\mathrm{V}}{\mathrm{L}}-\frac{3\mathrm{V}}{4\mathrm{L}}=3$

$\therefore \mathrm{ }\frac{\mathrm{V}}{4\mathrm{L}}=3$

$\therefore \frac{\mathrm{V}}{\mathrm{L}}=12\mathrm{ }$

When we close one end of the open pipe and make its length one-third of the original length, then its fundamental frequency is

$\mathrm{f}=\frac{\mathrm{V}}{4\left({\displaystyle \frac{\mathrm{L}}{3}}\right)}=\frac{3\mathrm{V}}{4\mathrm{L}}$

When the length of closed pipe is made$3$times, the fundamental frequency is

$\mathrm{f}\text{'}=\frac{\mathrm{V}}{4\left(3\mathrm{L}\right)}=\frac{\mathrm{V}}{12\mathrm{L}}$

Beats produced$=\mathrm{f}-\mathrm{f}\text{'}$

$=\frac{3\mathrm{V}}{4\mathrm{L}}-\frac{\mathrm{V}}{12\mathrm{L}}$

$=\frac{8}{12}.\frac{\mathrm{V}}{\mathrm{L}}=\frac{8}{12}\times 12$

$=8$